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Math Help - hyperplane equation

  1. #1
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    hyperplane equation

    Hi guys, i need some hints to solve this very difficult problem from vector calculus:
    hyperplane equation-hyperplane.png
    please, help me!

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  2. #2
    MHF Contributor

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    Re: hyperplane equation

    The problem is to find the equation of the hyperplane tangent to the ellipse x_1^2+ 2x_2^2+ 3x_3^2+ \cdot\cdot\cdot+ nx_n^2= \frac{n(n+1)}{2} at the point (-1, -1, -1, \cdot\cdot\cdot, -1).

    Now, what is your difficulty? Can you find the gradient of the function? That will give a vector perpendicular to the ellipse at the give point. Do you know how to write the equation of a hyperplane given a normal vector and point?
    Thanks from frankitm
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